Question

What is the 32nd term of the arithmetic sequence where a1 = 15 and a13= -57?

Answer 1

if we shift the index to start at a0 ... this might be easier to see

Answer 2

a0 = 15 +d(0)
a1 = 15 + d(1)
a2 = 15 + d(2)
a3 = 15 + d(3)
a4 = 15 + d(4)
a5 = 15 + d(5)

an = 15 + dn ; but keep in mind the shift

Answer 3

a13 is a12:

a12 = -57

-57 = 15 + d(12)

solve for d

Answer 4

then use it to determine: a32 is shifted to a31

a31 = 15 + d(31)

Answer 5

d=-6

Answer 6

a31=-171

Answer 7

Thank you!

Answer 8

correct :)